I am interested in the stochastic processes driving pricechanges in markets,
in the appearance of bubbles in markets as well as in society and in the dynamics
of these processes lying behing the randomness. As a result I am puzzling on
the connection between decision-making as well as pricing processes and measurement-theory
on the other. Whether recreationally or potentially useful, I enjoy studying
the possibillities of generalizing game theory in a meaningful way into quantum game theory. Last but not least I am interested in the geometries of spanning
trees of correlations between pricechanges of assets or commodities
and questions regarding the embedding of those geometries in 2 or higher-dimensional
manifolds. Technically speaking I am interested in finding out which random
geometries could be made usefull in the (risk-)analysis of portfolios of stocks
, options and/or assets.

2] Gravitational physics & the Standard Model: or "What is Spin?"

In the recent past I worked on gravitational physics in several ways. In 2007
with my student Ivo Sturm & I computed the boundstate energies and decay-rates
of fermions around rotating blackholes (Kerr blackholes). Considering the bound
state of
a spin 1/2 fermion with a blackhole as a model system in which tweaking of
parameters allows a smooth transition between the regime where non-relativistic
QM applies down to a regime where full quantum gravity wouldbe required. Our
approximation methods only allowed us to infer the (till that moment unknown)
existence of those boundstates for relativistic systems in which particle-creation
plays no substantial role.

Spin plays the role of a fundamental angular momentum in quantum mechanics,
yet in gravitational systems it can also act as a source of torsion, which
is a second deformation of spacetime geometry next to curvature. Einsteins
theory of General Relativity describes torsion-free but curved spacetime interacting
with matter. With several students (Thomas Rot, Wilke vd Schee, Jelle Aalbers Rutger-Jan Lange, 2007-2009) I investigated
whether the Newman-Janis algorithm (that "mysteriously" relates rotating and
non-rotating blackhole geometries) can be seen to induce torsion in intermediate
stages of the algorithm.

In the theory of the weak interactions spin takes on yet another role as it
non-trivially enters the way in which leptons interact and the way charges
are assigned to these particles. The keyword here is chirality. With Inge
Kielen (2009) I studied an earlier idea on using geometric algebras (or Clifford
algebras with an added interpretation) to possibly clarify the spacetime-geometric role of these charge-assignments.

Particles with half-integer spin are described by variants of the Dirac equation.
Using geometric algebra this Dirac equation in spacetime can be closely associated
to classical equations of motion of spinning, massive, particles in the eigen-rotor
form. With Misha Spelt & Selma Koghee (2009) I formulated an eigen-rotor formulation of the
dynamics of relativistic strings in (ordinary) spacetime that provides and
even closer association of the Dirac equation with relativistic classical dynamics.

3] Non-equilibrium quantum field theory

I am interested in the non-equilibrium formulation of quantum field theory
as in such a context many of the familiar notions of particle physics lose
their immediate physical interpretation. Non-equilibrium dynamics requires
us to completely rethink what a particle is, how it's properties are co-determined
by the surrounding medium and how the lack of isolation (or the persistance
of interactions) changes our view of the identity of particles. Our intuitive
understanding of reality largely rests on non-relativistic classical physics
whereas the extreme conditions in high-energy phenomena such as quark-gluon
plasma's, or close to blackholes, or near the origin of the universe itself,
require the language of relativistic quantum field theory involving a high
density of excitations. In 1995 (as part of my PhD thesis) is found a infinite
family of (Ward-like) identities satisfied by non-equilibrium qft's, unfortunately
without proper application so far. In 1997 I showed for a simple model system that non-relativistic limit and classical limit do
not
neccesarilly
commute.